Final answer:
The nth term of the given sequence is obtained by adding 30 to the previous term.
Step-by-step explanation:
To find the nth term of the sequence 11, 41, 71, 101, 131, we can observe that each term is obtained by adding 30 to the previous term. Therefore, we can represent the nth term as follows:
nth term = 11 + (30 x (n - 1))
For example, if we want to find the 5th term, we substitute n = 5 into the formula:
5th term = 11 + (30 x (5 - 1)) = 11 + (30 x 4) = 11 + 120 = 131
Looking at the sequence, it seems like the numbers are increasing by 30 each time (41 - 11 = 30, 71 - 41 = 30, and so on).
So, to find the
�
�
ℎ
n
th
term of this sequence, you can use the formula for arithmetic sequences:
nth term
=
�
+
(
�
−
1
)
×
�
nth term=a+(n−1)×d
Where:
�
a is the first term of the sequence (in this case,
�
=
11
a=11)
�
n is the term number you want to find
�
d is the common difference between consecutive terms (here,
�
=
30
d=30)
Let's find the
�
�
ℎ
n
th
term of this sequence using this formula. If you're looking for a specific term, let's say the 10th term:
nth term
=
11
+
(
10
−
1
)
×
30
nth term=11+(10−1)×30
nth term
=
11
+
9
×
30
nth term=11+9×30
nth term
=
11
+
270
nth term=11+270
nth term
=
281
nth term=281
So, the 10th term of this sequence is 281. You can use this formula to find any term in this sequence by substituting the appropriate value for
�
n.